7/(y^2-4)-4/(y+2)=5/(y-2)

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Solution for 7/(y^2-4)-4/(y+2)=5/(y-2) equation:


D( y )

y+2 = 0

y^2-4 = 0

y-2 = 0

y+2 = 0

y+2 = 0

y+2 = 0 // - 2

y = -2

y^2-4 = 0

y^2-4 = 0

1*y^2 = 4 // : 1

y^2 = 4

y^2 = 4 // ^ 1/2

abs(y) = 2

y = 2 or y = -2

y-2 = 0

y-2 = 0

y-2 = 0 // + 2

y = 2

y in (-oo:-2) U (-2:2) U (2:+oo)

7/(y^2-4)-(4/(y+2)) = 5/(y-2) // - 5/(y-2)

7/(y^2-4)-(4/(y+2))-(5/(y-2)) = 0

7/(y^2-4)-4*(y+2)^-1-5*(y-2)^-1 = 0

7/(y^2-4)-4/(y+2)-5/(y-2) = 0

(7*(y+2)*(y-2))/((y^2-4)*(y+2)*(y-2))+(-4*(y^2-4)*(y-2))/((y^2-4)*(y+2)*(y-2))+(-5*(y^2-4)*(y+2))/((y^2-4)*(y+2)*(y-2)) = 0

7*(y+2)*(y-2)-4*(y^2-4)*(y-2)-5*(y^2-4)*(y+2) = 0

15*y^2-4*y^3-5*y^3-10*y^2+16*y+20*y-60+40 = 0

5*y^2-9*y^3+36*y-20 = 0

5*y^2-9*y^3+36*y-20 = 0

5*y^2-9*y^3+36*y-20 = 0

{ 1, -1, 2, -2, 4, -4, 5, -5, 10, -10, 20, -20 }

1

y = 1

5*y^2-9*y^3+36*y-20 = 12

1

-1

y = -1

5*y^2-9*y^3+36*y-20 = -42

-1

2

y = 2

5*y^2-9*y^3+36*y-20 = 0

2

y-2

10-9*y^2-13*y

5*y^2-9*y^3+36*y-20

y-2

9*y^3-18*y^2

36*y-13*y^2-20

13*y^2-26*y

10*y-20

20-10*y

0

10-9*y^2-13*y = 0

DELTA = (-13)^2-(-9*4*10)

DELTA = 529

DELTA > 0

y = (529^(1/2)+13)/(-9*2) or y = (13-529^(1/2))/(-9*2)

y = -2 or y = 5/9

y in { -2, 5/9, 2}

(y+2)*(y-5/9)*(y-2) = 0

((y+2)*(y-5/9)*(y-2))/((y^2-4)*(y+2)*(y-2)) = 0

((y+2)*(y-5/9)*(y-2))/((y^2-4)*(y+2)*(y-2)) = 0 // * (y^2-4)*(y+2)*(y-2)

(y+2)*(y-5/9)*(y-2) = 0

( y+2 )

y+2 = 0 // - 2

y = -2

( y-2 )

y-2 = 0 // + 2

y = 2

( y-5/9 )

y-5/9 = 0 // + 5/9

y = 5/9

y in { -2}

y in { 2}

y = 5/9

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